Solve for $x$ and $y$ by deriving an expression for $y$ from the second equation, and substituting it back into the first equation. $\begin{align*}5x-6y &= 4 \\ -x-3y &= 9\end{align*}$
Explanation: Begin by moving the $x$ -term in the second equation to the right side of the equation. $-3y = x+9$ Divide both sides by $-3$ to isolate $y$ $y = {-\dfrac{1}{3}x - 3}$ Substitute this expression for $y$ in the first equation. $5x-6({-\dfrac{1}{3}x - 3}) = 4$ $5x + 2x + 18 = 4$ Simplify by combining terms, then solve for $x$ $7x + 18 = 4$ $7x = -14$ $x = -2$ Substitute $-2$ for $x$ back into the top equation. $5( -2)-6y = 4$ $-10-6y = 4$ $-6y = 14$ $y = -\dfrac{7}{3}$ The solution is $\enspace x = -2, \enspace y = -\dfrac{7}{3}$.